Question

An economist is studying the job market in Denver area neighborhoods. Let x represent the total number of jobs in a given neighborhood, and let y represent the number of entry-level jobs in the same neighborhood. A sample of six Denver neighborhoods gave the following information (units in hundreds of jobs).

x	16	33	53	28	50	25
y	2	3	5	5	9	3

Given: Σx = 205    Σy = 27    Σx² = 8063    Σy² = 153    Σxy = 1061 r ≈ 0.758.

(c) Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)

x	= ___
y	= ____
	= ____	+ ___ x

(e) Find the value of the coefficient of determination r². What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r² to three decimal places. Round your answers for the percentages to one decimal place.)

r2 =
explained	%
unexplained	%

(f) For a neighborhood with x = 32 hundred jobs, how many are predicted to be entry level jobs? (Round your answer to two decimal places.) ______ hundred jobs

Answer 1

c)

X̅=ΣX/n =	34.17
Y̅=ΣY/n =	4.50
ŷ =	0.031+0.131x

e)

coefficient of determination r2 =				0.575
explained =				57.5%
unexplained=				42.5%

f)

predicted value =0.031+0.131*32=

4.22